    4.  VectorValued Reinforcement Learning   post by Patrick LaVictoire 993 days ago  Ryan Carey and Jessica Taylor like this  1 comment  
 In order to study algorithms that can modify their own reward functions, we can define vectorvalued versions of reinforcement learning concepts.
Imagine that there are several different goods that we could care about; then a utility function is represented by a preference vector \(\vec\theta\). Furthermore, if it is possible for the agent (or the environment or other agents) to modify \(\vec \theta\), then we will want to index them by the timestep.
Consider an agent that can take actions, some of which affect its own reward function. This agent would (and should) wirehead if it attempts to maximize the discounted rewards as calculated by its future selves; i.e. at timestep \(n\) it would choose actions to maximize
\begin{eqnarray} U_n = \sum_{k\geq n} \gamma_k \vec{x}_k\cdot\vec{\theta}_k\end{eqnarray}
where \(\vec x_k\) is the vector of goods gained at time \(k\), \(\vec \theta_k\) is the preference vector at timestep \(k\), and \(\gamma_k\) is the time discount factor at time \(k\). (We will often use the case of an exponential discount \(\gamma^k\) for \(0<\gamma<1\).)
However, we might instead maximize the value of tomorrow’s actions in light of today’s reward function,
\begin{eqnarray} V_n = \sum_{k\geq n} \gamma_k\vec{x}_k\cdot\vec{\theta}_{n} \end{eqnarray}
(the only difference being \(\vec \theta_n\) rather than \(\vec \theta_k\)). Genuinely maximizing this should lead to more stable goals; concretely, we can consider environments that can offer “bribes” to selfmodify, and a learner maximizing \(U_n\) would generally accept such bribes, while a learner maximizing \(V_n\) would be cautious about doing so.
So what do we see when we adapt existing RL algorithms to such problems? There’s then a distinction between Qlearning and SARSA, where Qlearning foolishly accepts bribes that SARSA passes on, and this seems to be the flip side of the concept of interruptibility!
 
    7.  A simple model of the Löbstacle   post by Patrick LaVictoire 1501 days ago  Abram Demski and Jessica Taylor like this  discuss  
 The idea of the Löbstacle is that basic trust in yourself and your successors is necessary but tricky: necessary, because naively modeling your successor’s decisions cannot rule out them making a bad decision, unless they are in some sense less intelligent than you; tricky, because the strongest patches of this problem lead to inconsistency, and weaker patches can lead to indefinite procrastination (because you always trust your successors to do the thing you are now putting off). (For a less handwavy explanation, see the technical agenda document on Vingean reflection.)
It is difficult to specify the circumstances under which this kind of selftrust succeeds or fails. Here is one simple example in which it can succeed, but for rather fragile reasons.
 
   9.  Agents that can predict their Newcomb predictor   post by Patrick LaVictoire 1537 days ago  Jessica Taylor likes this  4 comments  
 There’s a certain type of problem where it appears that having more computing power hurts you. That problem is the “agent simulates predictor” Newcomb’s Dilemma.
As Gary Drescher put it:
There’s a version of Newcomb’s Problem that poses the same sort of challenge to UDT that comes up in some multiagent/gametheoretic scenarios.
Suppose:
 The predictor does not run a detailed simulation of the agent, but relies instead on a highlevel understanding of the agent’s decision theory and computational power.
 The agent runs UDT, and has the ability to fully simulate the predictor.
Since the agent can deduce (by lowlevel simulation) what the predictor will do, the agent does not regard the prediction outcome as contingent on the agent’s computation. Instead, either predictonebox or predicttwobox has a probability of 1 (since one or the other of those is deducible), and a probability of 1 remains the same regardless of what we condition on. The agent will then calculate greater utility for twoboxing than for oneboxing.
Meanwhile, the predictor, knowing that the the agent runs UDT and will fully simulate the predictor, can reason as in the preceding paragraph, and thus deduce that the agent will twobox. So the large box is left empty and the agent twoboxes (and the agent’s detailed simulation of the predictor correctly shows the predictor correctly predicting twoboxing).
The agent would be better off, though, running a different decision theory that does not twobox here, and that the predictor can deduce does not twobox.
EDITED 5/19/15: There’s a formal model of this due to Vladimir Slepnev where the agent and the predictor both have different types of predictive powers, such that in some sense they each know how the other will act in this universe. We’ll write this out along with another case where things work out properly.
(One algorithm has more computing power, but the other has stronger axioms: in particular, strong enough to prove that the other formal system is sound, as ZFC proves that PA is sound.)
In one of the following cases, proofbased UDT oneboxes for correct reasons; in the other case, it twoboxes analogously to the reasoning above.
 
      14.  Meta the goals of this forum   post by Patrick LaVictoire 1594 days ago  Benja Fallenstein, Jessica Taylor and Luke Muehlhauser like this  1 comment  
 Summary: We’re planning to publicize and open up the forum very soon, and so it’s a good time to discuss what we would like this forum to achieve, how we plan for moderation to work, and what discussions are ontopic.
Currently, this forum is readonly for everyone except for a few veterans of the mailing list it replaces. In a few days, we’re planning to open up posting (in a tiered way, similar in spirit to the tiered privileges of MathOverflow), and the comments and Likes of the full members will play a material role in moderating the community. So it’s a good time for those of us who are already here to discuss our goals for the forum, so that we stand a better chance of coordinating.
 
    

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